Semiconductor Physics and Devices: Basic Principles, 4th edition
Chapter 1
By D. A. Neamen
Exercise Solutions
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Chapter 1
TYU 1.2
(a) Number of atoms per (100) lattice plane
1
 4  1
4
1
1
Surface Density  2 
2
a
4.65 10 8
Exercise Solutions
Ex 1.1
(a) Number of atoms per unit cell
1
1
 8   6  4
8
2
4
4
(b) Volume Density  3 
a
4.25  10 8



3
 5.2110 22 cm 3
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Ex 1.2
Intercepts of plane; p=1, q=2, s=2
1 1 1 
Inverse;  , , 
1 2 2 
Multiply by lowest common denominator,
 211 plane
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Ex 1.3
(a) Number of atoms per (100) plane
1
 1 4  2
4
2
2
Surface Density  2 
a
4.25 10 8


2
= 4.62 10 cm
(b) Number of atoms per (110) lattice plane
1
 4  1
4
Surface Density
1
1


a  a 2 4.65 10 8 2 2
14
  

2
 3.27 10 cm
(c) Number of atoms per (111) lattice plane
1 1
 3 
6 2
1
Lattice plane area  bh
2
14
where b  a 2
 

ha 2


2
2
2
1
 
 a 2 
2
 
1/ 2
1/ 2
Test Your Understanding Solutions
1 
3

  2a 2  a 2   a
2 
2

Then lattice plane area
 3
1
  3 a2
 a 2 a
 2
2
2


Surface Density
1
2

 2.67 1014 cm 2
2
3
4.65 10 8
2
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TYU 1.1
TYU 1.3
 1.111015 cm 2
(b) Number of atoms per (110) plane
1
1
 2  4  2
2
4
Surface Density
2
2


a  a 2 4.25 10 8
  
 

2
2
2
 7.83 10 cm
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14
Number of atoms per unit cell  8 
Volume Density  4  10 22 
1
1
8
1
a3
o
 a  2.92 10 8 cm  2.92 A
o
Radius  r  a 2  1.46 A
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

o
(a) For (100) planes, distance  a  4.83 A
(b) For (110) planes, distance
o
a 2 4.83 2

 3.42 A
2
2
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
Semiconductor Physics and Devices: Basic Principles, 4th edition
Chapter 1
By D. A. Neamen
Exercise Solutions
______________________________________________________________________________________
TYU 1.4
(a) 8 corner atoms
(b) 6 face-centered atoms
(c) 4 atoms totally enclosed
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TYU 1.5
Number of atoms in the unit cell
1
1
 8  6  4  8
8
2
8
8
Volume Density  3 
a
5.43  10 8


3
 510 22 cm 3
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